Example of an axioms in G3Cp

Question

Would $$A,B,C \Longrightarrow C,A$$ be an axiom in G3Cp? I ask because B is not on both sides and I am not sure if that makes a difference or not?

Answer 1

See :

• Sara Negri & Jan von Plato, Structural Proof Theory (2001), page 49;

in the sequent calculus G3cp of classical propositional logic, the logical axioms are :

$P, \ \Gamma \Longrightarrow \Delta, \ P$

where $\Gamma$ and $\Delta$ are finite multisets (they can be empty).

Thus, $A, B, C \Longrightarrow C, A$ is an axiom, where $\Gamma = \{ B, C \}$ and $\Delta = \{ C \}$.